This paper makes several contributions. First, we develop a new model of adaptive experiments. This model combines the information structure of a Bayesian linear contextual bandit problem [1]} with the population level decision objective of [2]} or [3]}. We highlight in Section  that substantial challenges arise when the context sequence may follow a nonstationary pattern. We describe two examples of this form. Example REF  describes a weeklong experiment where the rewards an arm generates depend on the day. In this case, the source of nonstationarity is an observed exogenous factor. In Example REF , we show that latent (i.e. unobserved) confounders can be modeled by taking the observed context to be an indicator of the time at which a decision was made. An exogenous Gaussian process then influences arms' rewards and we give examples of how specifying a covariance structure allows a modeler to specify the severity of plausible nonstationarity. Section  shows that natural MAB algorithms fail in such problems and gives insight into why.
